Digital communications systems often include a modem. A modem is used for modulation and/or demodulation of digital data signals. In modulation, the digital data signal is encoded into an analog format signal (e.g., a carrier wave or radio signal), and in demodulation, the digital signal is extracted from an analog format signal. Modulation formats can include, for example, phase shift keying, amplitude shift keying, frequency shift keying, and combinations thereof.
Modems are often implemented using digital signal processing techniques which operate on digitized discrete time samples of the signals. Digital signal processing techniques can be realized in hardware, software, or a combination thereof. High data rates are often desired, which in turn translates into high processing speed requirements on the modem implementation.
Various constraints, such as Nyquist's theorem apply to the digital sampling of signals, setting limits on the sampling rates which can be used. Previously, modems have operated using sample rates in excess of two samples per symbol. Limitations in hardware processing speeds (e.g., the digital signal processing subsystem, analog to digital converters, and digital to analog converters) have set upper limits to the data rates at which modems can operate. While continuous advances in technology have allowed for continually increasing data rates, there is a desire to find more efficient techniques which allow higher data rates to be provided within existing technology constraints.